The article considers a linear consecutive-k-out-of-n: F system and a linear connected-(r, s)-out-of-(m, n): F system. It is assumed that the components are identical and the failure times of components follow an exponential distribution. The system is continuously monitored and the component failure can be known at any time. A preventive maintenance policy is proposed, and it is based on the system critical condition which is related to the number of working components in the minimal cut sets of the system. If there is at least one minimal cut set which consists of only one working component, the system is maintained preventively after a certain time interval and the failed components are replaced with the new ones to prevent the system failures. The expected cost rate is used as an optimization criterion. The expected cost rate is estimated by simulation and numerical examples are studied. The numerical analyses are exploratory and not generalizable.

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Purpose The purpose of this paper is to develop a preventive maintenance policy with continuous monitoring for a circular consecutive-k-out-of-n: F systems. A preventive maintenance policy is developed based on the system critical condition which is related to the number of working components in the minimal cut sets of the system. If there is at least one minimal cut set which consists of only one working component, the system is maintained preventively (PM) after a certain time interval and the failed components are replaced with the new ones to prevent the system failures. If the system fails prior to the preventive maintenance, the system is correctively maintained (CM) immediately by replacing the failed components. Design/methodology/approach The mathematical function of the expected cost rate for the proposed maintenance policy is derived. The costs of PM, CM, and replacement per component are considered. The optimal maintenance parameter, which is the PM interval, is obtained by enumeration, and the numerical studies are shown with various system and cost parameters. The performance of the proposed policy is evaluated by comparing its expected cost rate to those of the no-PM and age-PM policies. The percentage of cost increase from the no-PM and age-PM policies to the proposed PM policy is calculated and this value can represents how important the continuous monitoring in this policy. Findings The proposed policy outperforms other policies. When the cost of CM is high and the cost of PM is low, the proposed PM policy is more suitable. Research limitations/implications The system consists of identical components and the component failure times follow an exponential distribution. Continuous monitoring is considered, which means that the component states can be known at any time. Three cost parameters, cost of PM, CM, and replacement per component, are considered. Originality/value This paper shows a maintenance problem for circular consecutive-k-out-of-n: F systems. Many studies on this system type focused on the reliability estimation or system design problem. Previous study with this policy (Endharta and Yun, 2015) has been developed for linear systems, although the study used a simulation approach to estimate the expected cost rate. Also, Endharta et al. (2016) considered a similar method for the different types of system, which is linear consecutive-k-out-of-n: F system.

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Linear consecutive-k-out-of-n: F systems are considered. It is assumed that the components are independent and the component failure times follow an exponential distribution with identical failure rate. It is also assumed that there are only two component states (working and failed) and we can know the component state at any time. If there is at least one minimal cut set consisting of one working component, the system will be preventively maintained after a certain time interval. If the system fails before reaching the preventive maintenance (PM) time, the failed components are replaced by the new ones. The optimal PM interval time which minimizes the expected cost rate is obtained. The performance of the proposed policy is evaluated by comparing the expected cost rate of the proposed policy with those of corrective maintenance (CM) and age PM policy.